Automatic control systems for optimizing heat transfer to a fluid flowing through parallel connected heat exchangers



May 30, 1967 E. A. WEISS 3,322,938

AUTOMATIC CONTROL SYSTEMS FOR OPTIMIZING HEAT TRANSFER TO A FLUID FLowTNG THROUGH PARALLEL CONNECTED HEAT EXCHANGERS Filed Feb.

7 Sheets-Sheet l ATTORNEY May 3o, 1967y E. A. WEISS AUTOMATIC CONTROL SYSTEMS FOR OPTIMIZING HEAT TRANSFER TO A '7 Sheets-Sheet 2 Filed Feb. 15, 1963 w .Sm

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ATTORNEY E. A. wl-:lss 3,322,938 MS FOR OPTIMIZING HEAT TRANSFER TO A PARALLEL CONNECTED HEAT EXCHANGERS 7 Sheets-Sheet May 30, 1967 AUTOMATIC CONTROL sYsTE FLUID FLOWING THROUGH Filed Feb. 15, 1963 6I Storage Unit n.. n. hurn w SCIIII S 2 7 7/ 6 T A dd n mIINIwm nvv DC 4 6 e M.. mm II .MU 9/ 1 f. l mf. Uk SC P 9 6 I I I Il@ 6 6/ u IIII/IIIIIIIIIIIIIL C n I. k q e l I I l I I I I I I I I I II I RC s e 6 INVENTOR. ERIC A. WEISS ATTORNEY May 30, 1967 E. A. WEISS 3,322,938 AUTOMATIC CONTROL SYSTEMS FOR OPTIMIZING HEAT TRANSFER TO A FLUID FLOWING THROUGH PARALLEL CONNECTED HEAT EXCHANGERS Filed Feb. l5, 196s 7 sheets-sheet L;

v INVENTOR ERIC A. WEISS BY ATTORNEY May 30, 1967 AUTOMATIC CONTROL SYSTEMS EOR OPTIMTZING HEAT TRANSFER TO A FLUID ELOWTNG THROUGH PARALLEL CONNECTED HEAT EXOHANGERS Filed Feb. l5, 1965 E. A* WEISS Coplfolcnm 7 Sheets-Sheet 5 I I ConIroI Scheme I I V I I I I Heai l I Exchanger I I I x I I I 92 i I I Heat I I I I Exchanger I Y I I I \I I I I 9| Heut 93 I Exchanger I I z I I Heat Hear Exchanger Exchanger X X Heat Heat Exchanger Exchanger Y Y Heat Heat Exchanger Exchanger Z z INVENTOR ERIC A. WEISS ATTORNEY May 30, 1967 E. A. WEISS 3,322,938

AUTOMATIC CONTROL SYSTEMS FOR OPTIMIZING HEAT TRANSFER TO A FLUID FLOWING THROUGH PARALLEL CONNECTED HEAT EXCHANGERS Filed Feb. 15, 1965 7 Sheets-Sheet 6 Fig, 8 Fig 9 Heat A Heat Exchanger Exchanger Heai Heat Exchanger Exchanger Heat Heat Exchanger Exchanger Z Z ToaI (Till Input 5 E sfBUm Heut 94/ ....I Exchanger /95 96 x Tx 97 I fx 6 I5 Blend Adder computer Y II fzV Heat 'rz -l Exchanger Fig. /0 Mm INVENTOR.

ERIC A. WEISS ATTOR NEY May 30, 1967 E. A. WEISS AUTOMATIC CONTROL SYSTEMS FOR OPTIMIZING HEAT TRANSFER TO A FLUID FLOWING THROUGH PARALLEL CONNECTED HEAT EXCHANGERS Filed Feb. 15, 1965 F/gn' I l I I Heat Exchanger Y I I II I I I. I

7 Sheets-Sheet 7 Control SchemelI II Heat Exchanger Z Heat Exchanger Control Sch mem He a1 Exchanger Heat Exchanger I ,I I'

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ConIrol Scheme I! I --1 I' Heat Exchanger I I v I I I I Heat Exchanger I I W I I I I I I I I I I I I INVENTOR I I I I I Y ERIC A. wEIss Away/(ZW ATTORNEY United States Patent O AUTGMATIC CONTRGL SYSTEMS FOR OZ- lNG HEAT TRANSFER T A FLUID FLGWNG THRQUGH PARALLEL CQNNECTED HEAT EX- CHANGERS Eric A. Weiss, Springfield, Pa., assigner to Sun Oil Company, Philadelphia, Pa., a corporation of New Jersey Fiieti Feb. 15, 1963, Ser. No. 258,843 7 Claims. (Cl. 23S-150.1)

This invention relates to automatic control systems, and more particularly to methods and apparatus for optirnizing or maximizing the total heat transferred to a fluid flowing through parallel-connected heat exchangers. The optimizing is elliected automatically and continuously.

It is common practice, particularly in petroleum refining, to use heat exchangers connected in parallel with each other, That is to say, a single stream of fluid is divided into two or more branches, following which division each branch is passed through a separate heat exchanger, and thereafter the streams are recombined into a single stream. The other sides of such parallel-con nected exchangers may or may not be operated in parallel with each other. With parallel-connected operation, there arises the problem of selecting and maintaining the optimum division of ilow among the several exchangers, so as to obtain the maximum heat transfer to the fluid, which is equivalent to achieving the maximum temperature of the final recombined stream. The problem of maintaining the best or optimum division of ow is not simply one of maintaining a constant ilow, or even a constant ilow ratio, since variations in total iluid flow, variations in iluid composition, variations in the ilow and composition of the lluids on the other sides of the exchangers, and variations in the fouling and corrosion of the exchangers themselves will require changes in the oW division, if the best possible heat transfer is to be maintained in spite of all such variations.

The economic gains from continuous optimization of heat transfer are particularly large in situations where very large flows are passing through a set of parallelconnected heat exchangers. For example, a crude oil heat exchange network which is transferring 80 million B.t.u./ hr. and which is only off optimum costs its operator about $15,000 per year in extra fuel cost to heat the crude oil; this extra fuel cost could be entirely eliminated if the heat exchange network were optimized.

An object of this invention is to provide a novel automatic control system.

Another object is to provide an automatic control sysd tem for continuously optimizing the division of lluid ilow between two or more parallel-connected heat exchangers.

A further object is to provide a method and apparatus for maximizing the total heat transferred to a iluid flowing through two parallel-connected heat exchanger assemblies one of which may comprise a plurality of exchangers connected in parallel,

The objects of this invention are accomplished, briefly, in the following manner: Certain key variables in a heattransfer system are measured, and the information thus obtained, together with information about certain characteristics of the heat exchangers used, is fed into a computer which arithmetically combines the items of information in accordance with a certain mathematical formula, thereby to develop a signal proportional to the rate of change of the total heat transferred with a change in the iluid ilow through one exchanger. This latter signal indicates the direction and amount of ilow variation needed to produce the optimum heat transfer, and it is used to manipulate a ilow controller to adjust the flow between the exchangers so as to bring about this optimum heat transfer.

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A detailed description of the invention follows, taken in conjunction with the accompanying drawings, wherein:

FIG. l is a schematic diagram of one embodiment of the invention;

FIG. 2 is a similar diagram of another embodiment;

FIG. 3 is a schematic diagram of a system for automatically determining heat exchanger characteristics;

FIG. 4 is a schematic diagram of a sequenced type of control system;

FIGS. 5-10 illustrate various Iarrangements of three parallel-connected heat exchangers; and

FIG. ll illustrates an arrangement of eight parallelconnected heat exchangers.

Consider a pair of heat exchangers 1 and 2 connected in parallel on one side, as shown in FIG. l. The iluid stream ilowing in pipe 3 is divided into two branches, one branch (the upper) ilowing through heat exchanger 1 and the other branch flowing through heat'exchanger 2.' Thereafter, the two streamsare recombined into la single stream llowing in pipe 4. The mass flow rate through exchanger 1 is A and the mass ilow rate through exchanger 2 is B. The total ilow A+B is a constant; how this total ilow might be maintained constant Will be explained hereinafter.

The heated-fluid ilows on the other side of each exchanger (by means of which heat is supplied to the iluid ilows A and B) are assumed to be constant in quantity, composition, and inlet temperature, but ,are not necessarily the same for the tow exchangers. Y

The problem is to determine the ratio of flow A to ilow B required to obtain the maximum temperature of the total mixed stream A+B after exchange, this latter temperature being denoted by To.

The temperature of the mixed stream A+B in pipe 3 before exchange is Ti. The iluid outlet temperature of exchanger 1 is TA and that of exchanger 2 is TB. The average specific heat for the material in exchanger 1 is SA and for the material in exchanger 2 is SB; these specific heats are different because the temperatures TA and TB will in general be different from each other. Then, the expression for the total heat transferred is The change in heat transferred for a change in ilow division between the branches may be found by differentiating Q (above) with respect to A and using the condi- ,n SA= TA ,+670 2.1 Specificzgaotvity of fluid as presented in Industrial & Engineering Chemistry, 1927, page 824, we obtain, after differentiating Equation l above, and then rearranging, substituting for SA and SB and gathering terms,

@ TB dA dA In Equation 3,

2.1 Specific gravity In connection with Equation 2, it is noted that the onstants 670 and 2030 are appropriate for petroleum luids. For other uids, an equation of the same form Iould apply, but the constant might be diterent.

Equation 3 contains the term dTA/ dA. This is a characeristic of the design construction and condition of heat xchanger 1 and of the nature and temperatures of both luids flowing in it. It is experimentally ydetermined (this iay be done automatically, as will be described hereinfter) or calculated, and it represents the ratio between he incremental change in the outlet temperature of the .uid and the incremental change in ow which caused Y he temperature change. It may be thought of as the slope f the fluid outlet temperature vs. uid ow characteristic f the exchanger. Since an increase in flow in an exhanger causes a decrease in the outlet temperature of :le same exchanger, dTA/dA is negative. An expression TB/dB is defined in the same way for the exchanger ontaining ow B. Since the sum A+B is held constant, ny incremental change in B is equal and opposite to any icremental change in A. Consequently,

dTB/dA=-dTB/dB nd dTB/dA is always positive. This latter term appears 1 Equation 3.

In accordance with a basic concept of differential alculus, Q (the total heat transferred) is a maximum rhen dQ/dA=0. Equation 3 is a formula for dQ/dA.

The various embodiments of the present invention inolve measuring the parameters of the formula for Q/dA, Equation 3 above, or a simplification (given ereinafter) of this formula, and systematically adjusting ow A or flow B, or both, to bring dQ/ dA to zero. This iaximizes or optimizes Q, the total heat transferred.

Refer again to FIG. 1. This figure is a schematic epresentation of a first embodiment of this invention. l owmeter 5 is connected into the (upper) branch line :ading to reat exchanger 1, to measure the flow A, a ow transmitter 6 being connected to the owmeter 5 to adicate the actual fiow, as well as to transmit the flow ieasurement to other units. It is assumed, for purposes if explanation, that flowmeter 5 is of the so-called oriiice vpe, although it could be of the turbine type, or other uitable type. Orifice-type owmeters give indications proortional to the square of the Volume flow rate, so to roduce a voltage (signal) proportional to A, the output if ow transmitter `6 is fed into a square root circuit 7, which extracts the square root of the signal fred thereto. ilus, the output 8 of the circuit 7 represents A, the ow rate through heat exchanger 1. Of course, if some ther type of owmeter were used at 5, the square root ircuit 7 would not be needed.

Although orifice-type flowmeters give indications proortional to the square of the volume flow rate, the volume ow rate is proportional to the mass flow rate for a laterial of fixed specific gravity. Under the conditions lustrated in FIG. l, the specific gravity is approximately onstant, so it may `be said that the output 8 of circuit 7 i 'substantially proportional to the mass ow rate through eat exchanger 1.

In general, it may be said that the ow rates referred i (in the theory on which this invention is based) are lass ow rates, so the physical embodiment of the inention must provide measuring means which will deteriine this rate, to a precision appropriate to the situation nd to the results desired. While many common owxeters (for example, orifice-plate types) actually measure olume flow rates, for small temperature changes in many Jmmercial liquids, volume ow rates are directly proortional to mass ow rates. However, for increased recision, volume flow rate measurements may be cor- :cted to mass ow rates by using the temperature of the owing stream in a calculation. This correction may be utomatically made within the ilowmeter, or it may be icluded in the control computations as previously dezribed.

If the invention is applied to heat exchangers involving gases or vapors, orifice-plate measurements must be corrected for the pressure of the ilowing stream, as well as for its temperature.

The ow A is regulated by a flow recording controller 9 having a mechanically-adjustable set point S.P. The flow transmitter 6 feeds its signal into controller 9. The flow A to heat exchanger 1 passes through a tlow control valve 1t?. Controller 9 controls or operates valve 10 (this control being represented by a dotteddine connection) to maintain ow A at the rate determined by the adjustment of the set point of controller 9. How this set point is automatically adjusted will be detailed hereinafter.

A flow meter 11, which may be an orifice-type meter similar to owmeter 5, is connected into the (lower) `branch line leading to heat exchanger 2, to measure the ow B, a ow transmitter 12 being connected to flowmeter 11. The output of iiow transmitter 12 is fed into a square root circuit 3, which extracts the square root of the signal fed thereto. The output 14 of the circuit 13 is approximately proportional to B, the mass ow rate through heat erchanger 2.

The fluid outlet temperature TA of exchanger 1 is measured by means of a temperature-sensing element 1S (illustrated as a thermocouple, for example) coupled to the outlet side of exchanger 1. Element 15 produces a signal proportional to the fluid outlet temperature of exchanger -1. Although illustrated as a thermocouple, the temperature-sensing element 15 may be a resistane thermometer, or some other suitable type of temperaturesensing element. The output signal of element 15' is fed to a multiplication circuit 16, which multiplies it by two, and is also fed to an add circuit 17 and to a subtract circuit 1S.

The iiuid outlet temperature TB of exchanger 2 is measured by means of a temperature-sensing element 19 which is coupled to the outlet side of exchanger 2, Element 19', which is similar to element 15 previously described, produces a signal proportional to the uid outlet temperature of exchanger 2. The output signal of element 19 is fed to a multiplication circuit 20', which multiplies it by two, and is also fed to the add circuit 17 and to the subtract circuit 18.

It should be apparent that the output 21 of circuit 16 is ZTA, and the output 22 of circuit 20 is ZTB. The add circuit 17 adds the two signals fed to its input, to produce an output 23 of TA-l-TB. The subtract circuit 18 subtracts the two signals fed to its input, to produce an output 24 of TA-TB- A generator 25 `generates a signal proportional to the constant K2, dened hereinabove, and the signal from Vgenerator 2S is fed to an add circuit 26 along with the output 22 of circuit 20, to produce at the output 27 of circuit 26 a signal K2-l-2TB. This latter signal is fed to a multiplication circuit 2S along with the output 14 of square root circuit 13. The multiplication circuit 28 multiplies the two signals thus fed to its input, to produce an output 29 of B(K2f-2TB).

The K2 signal from generator 25 is also fed to an add circuit 30 along with the output 21 of circuit 16, to produce at the output 31 of circuit 30 a signal Kg-l-ZTA. This latter signal is fed to a multiplication circuit 32 along with the output 8 of square root circuit 7. Circuit 32 multiplies the two signals fed to its input, to produce an output 33 of A(K2|2TA).

Adjustable variable dTA/dA is fed into the computer by means of a manually set knob (set to the value of this variable) which controls an adjustable generator 34. The dTA/dA signal is fed to a multiplication circuit 35 along with the output 33 of circuit 32. Circuit 35 produces an output 36 of dTA dA This latter output is fed to a final add circuit 37.'

Adjustable variation dTA/dA is fed into the computer by means of a manually set knob (set to the value of this variable) which controls an adjustable generator 38. The dTB/dA signal is fed to a multiplication circuit 39 along with the output 29 of circuit 2S. Circuit 39 produces an output 40 of This latter output is also fed to add circuit 37.

The K2 signal from generator 25 is also fed to an add circuit 41 along with the output 23 of circuit 17, to produce at the output 42 of circuit 41 a signal K2+TA+TB. This latter signal is fed to a multiplication circuit 43 along with the output 24 of subtract circuit 18. Circuit 43 produces an output 44 of (TA-TB) (K2+TA+TB). This latter output is also fed to add circuit 37.

The components 7, 13, 16, 17, 18, 20, 25, 26, 28, 30, 32, 34, 35, 37, 33, 39, 41, and 43 may be conventional and well-known electrical, mechanical, or pneumatic com- (Kai-271B) ponents, of the analog or digital type. Since the listed components perform an arithmetical combination (computation), they may be thought of as together comprising a computer.

The add circuit 37 adds together its three inputs 36, 40, and 44. By comparing the sum of such inputs with Equation 3 above, it may be seen that the (summed) output 45 of add circuit 37 is equivalent to or represents Speaking broadly, this quantity (output 45) is applied to a mechanical transducer which adjusts the set point of the flow controller in one branch (this is done on ow A in FIG. l

The expression or formula for dQ/dA, Equation 3, is such that the second and third terms in the square brackets are always negative (since dT A/dA is always negative) and the first and fourth terms always positive. Therefore, if dQ/ dA is negative, to bring this differential quantity to zero the magnitude of the second and third terms should be decreased. This can be done by decreasing A (which will increase B and therefore decrease TB). The foregoing provides information as t-o the proper control direction for ow A (with regard to the sign of dQ/ dA) in order to bring dQ/ dA t-o zero, thereby to maximize the t-otal heat transfer to the fluid owing through exchangers 1 and 2.

The mechanical transducer which adjusts the set point S.P. of the ow controller 9 of flow A is shown in FIG. 1 as a reversing motor 46, which is supplied by the output 45 of add circuit 37 and which mechanically adjusts the set point of controller 9, as schematically indicated by the dotted-line connection 47. The reversing motor 46 is a device which drives the ilow controller 9 set point slowly in a direction to decrease ow A whenever dQ/ dA is negative, and while it is negative, and reverses to drive this set point slowly in a direction to increase flow A whenever dQ/dA is positive, and While it is positive. The drive or mechanical adjustment of the set point will stop when dQ/dA is Zero, or close to zero.

The control system of FIG. 1 assumes that the total flow A+B is maintained constant by some control means additional to that described up to this point. The only reason for placing this requirement on the control system is so that any changes imposed by the computer portion of the control system on flow A Will be retiected in equal and opposite changes in ow B. One means for maintaining constant the total flow will now be described; this involves a iow control valve in the total stream pipe 3.

A floWmeter 48 is connected into line 3, to measure the total flow A+B, a ow transmitter 49 being connected to the owmeter 48 to indicate the actual flow in line 3. The flow A+B is regulated by a ow recording controller S0 having a manual set point adjustment S.P. The ow transmitter 49 feeds its signal into controller 50.

The total ow A+B passes through a ow control valve 51. Controller 50 controls or operates valve 51 (this control being represented by a dotted-line connection) to maintain the total ow A+B substantially constant, and at the rate chosen by the operator (by manual adjustment of the set point of controller 50).

Alternatively, the constant total ow control might be accomplished with a flow control valve controlling ow B.

In either case, the controller would maintain the total flow A+B constant, in spite of variations in flow A imposed by the automatic optimizing (maximizing) control system.

The requirement is that the total flow A+B be constant in spite of variations in flow A imposed by the automatic optimizing control system. However, it is not necessary that flow A+B be always unchanging Awith time. On the contrary, it is an object of the invention to optimize the heat transfer in spite of changes in the total ow A+B occurring at intervals which are long with respect to the time constant of the heat exchange system. In this connection, it is pointed out that the term heat exchange system includes the heat exchangers themselves, and also the control system associated with them. In most cases, the time constant of the heat exchangers would dominate the time constant of the heat exchange system.

Optimization of heat transfer will not necessarily be achieved when there are changes in the total ow A+B occurring at intervals which are short with respect to the time constant of the heat exchange system.

Equation 3 may be simplified by observing that K2=1340, while in such operations TA and TB will typically be in the range of to 400. Therefore, it can be said that the parenthetical parts of the four terms in Equation 3 are all approximately equal. That is to say,

(K2-l-T-l-TB) (K2-HTA) (Kz-l-ZTB) With this approximation,

dQ TA dTB MALTA-+AmtB'fm 4) Refer now to FIG. 2. This figure is a schematic representation of a second embodiment of the invention, illustrating a control system which mechanizes Equation 4. In FIG. 2, elements the same as those in FIG. 1 are denoted by the same reference numerals.

lust as in FIG. 1, the output S of the circuit 7 represents How A. This output is -fed to a multiplication circuit 52 along with the dTA/dA signal from adjustable generator 34. Circuit 52 produces an output 53 of This latter output is fed in a positive sense to a combining circuit 54.

As in FIG. 1, the output 14 of the circuit 13 represents flow B. This output is fed to a multiplication circuit 55 along with the dT B/ dA signal from adjustable generator 33. Circuit 55 produces `an output 56 of dTB Baa This Klatter output is fed in a positive sense to -circuit 54.

The TA signal from temperature-sensing ele-ment 15 is fed in a positive sense to circuit 54. The TB signal from temperature-sensing element 19 is fed in a negative sense to circuit 54.

From an examination of Equation 4 above, it can be seen that the four signals fed to circuit 54 correspond, respectively, to the Ifour terms on the right-hand side of this equation. The combining or summation circuit 54 alegbraically combines these four signals to produce an output 57 which is equivalent to or represents dQ/dA, according to the simplification for approximation given in Equation 4. The output 57 is supplied to the reversing motor 46, which mechanically adjusts t-he set point of conroller 9 for flow A. Just as in FIG. 1, the motor 46 drives he ow controller 9 set point in such a direction as to 'ring the dQ/dA signal at 57 to zero, or close to zero.

Comparing FIG. l with FIG. 2, it may `'be seen that the ystem of FIG. 2 provides a notable simplification of omputing components.

In yboth FIGS. 1 and 2, dTA/dA and dTB/dA were asumed to be determined lby calculation or measurement, nd were assumed to ybe put into the computer as an adlstable constant, for example, as a knob setting of repective generators 34 and 33. While this will in general e satisfactory, in some cases variations in the heat exhanger characteristics, or in the fluids involved, may be requent eno-ugh to justify an automatic determination of `TA/dA and dT B/dA. Broadly speaking, this automatic etermination may be effected by measuring the tempera- 1re difference across an exchanger and the flow through L, and deliberately introducing a small variation in the FIG. 3 is a schematic representation of a configuration /hereby the lautomatic determination is accomplished. n FIG. 3, a tlow controller 9, :ted from a owmeter 5 y way of ow transmitter 6, controls a valve in the ranch ow line through heat exchanger 1, to maintain constant ow -rate A. In the configuration of FIG. 3, 1e set point of flow controller 9 is adjustable in response 9 an impulse supplied thereto from a sequencer 66. A :mperaturesensing element 58 measures the temperature '1 of the fluid before the exchanger 1, and temperature :rising element measures the temperature TA of the uid after the exchanger. The output signals of elements 5 and 5S are fed to a subtract circuit 18, to form an utput 59 TA-Ti. This latter signal is normally fed by lay of lthe movable yarm of a `switch 60 to a storage unit 1, which stores its value. Storage unit 61 is of a type, .g., a magnetic drum or a capacitor, which stores the i-gnal `fed thereto in permanent yet erasable form; that i to say, the signal is permanent until it is erased and relaced by a new signal. For a digital system, the stored ignal would be in the form ofk a number; for an analog ystem, the stored signal would be in the form of a alue. The signal stored in unit 61 is fed to a subtract ciruit 62.

The output 8 of the square root circuit 7 -again repreents ow A. This latter signal is normally fed by way of 1e movable arm of a switch 63 to a storage unit 64, which `:ores its value. Unit 64 may be similar to unit 61, de- :ribed previously. The signal stored in unit 64 is ted 3 a subtract circuit 65.

A sequencer 66 is `coupled to the set point control of ontroller 9, to switches 60 and 63, and to `a division ciruit 67, as indicated by the dotted-line connections 68, 9, and 70 respectively. At wide intervals perhaps every our or more), sequencer 66 sends out a series of elec- 'ical, pneumatic, or mechanical impulses which (-by way f connection 68) change the ilow `controller 9 set point ,ightly (thereby to change slightly t-he flow through heat xchanger 1) and also (by way of connection 69) operate witches 60 and 63 to disconnect the inputs 59 and 8 from reir respective storage units.

Some time later, after the new flow and temperature onditions have lbecome stabilized (which later time may e determined either by elapsed time or by flow and ternerature measurement), sequencer 66 impulses switches 3 and 60 to their left-hand contacts, wherein the new sigal A is fed to subtract circuit 65 and the new signal 'A-Ti is fed to subtract circuit 62. It will Ibe noted that 1e other input to circuit 65 is obtained continuously from orage unit 64, and the other input to circuit 62 is obtined continuously from storage unit 61. At the same me that switches 63 and 60 are thus operated to their :ft-'hand contacts, impulses sent out from sequencer 66 by way of connection 70) result in actuation of division rcuit 67.

Using the subscripts 1 for conditions 'before the change 8 in flow and 2 for conditions after the change in flow, the subtract circuit 65 produces an output 71 of A1-A2, since A1 is fed continuously to circuit 65 from storage unit 64 and A2 is is fed to this same circuit when switch 63 is on its left-hand contact. The subtract circuit 62 produces -an output 72 of (TAl-TiQ-(TAg-Tiz), since (TA1-h) is fed continuously to circuit 62 from storage unit 61 and (TA2-T2) is fed to this same circuit when switch 69 is on its left-hand contact.

Division circuit 67 produces the quotient which is dTA/dA, since Tu ordinarily is equal to T12.

After the signal aTA/dA has been generated Iby circuit 67 in the above manner, sequencer 66 operates to restore the ow and all connections to normal. By adding com plexity to the sequencer, another measurement of dTA/dA could be made as a consequence of this return to normal.

The extension of the contiguration of FIG. 3 to the automatic measurement of dTB/dA would appear to be obvious.

The automatic measurement configuration of FIG. 3 may be added to either the computer of FIG. 1 or the computer of FIG. 2, lby allowing the dT li/dA and dTB/dA signals (obtained by the FIG. 3 scheme) to reset their corresponding adjustable variables (at 34 and 38 in FIGS. l and 2) after every series of sequencer impulses. It will :be necessary, with this combined arrangement, to cause the sequencer 66 to disable the optimizing computers of FIGS. l and 2 while testing for dT A/dA, in order to avoid undesirable interactions.

In connection with the control systems of FIGS. l and 2, previously described, it was stated that there is required some form of additional eontrolmeans, for maintaining the total ow A+B constant in spite of variations imposed by the computer portion of the control system on flow A. However, the control scheme of this invention can be applied to situations in which the flow A-l-B is not held constant, but is allowed to vary from time to time, so long as any variation imposed by the control scheme on ow A is reected in a variation in flow B which is equal in size (not percentage) and opposite in sign. That is, for every barrel per hour of increase caused by the control scheme in ow A, ow B must be decreased by a barrel, and vice versa. To state this in another way, in situations in which the total ow A+B varies from time to time, even at intervals which are short with respect to the heat exchange system time constant, the control scheme previously described will function properly if means are provided to vary flow B equally and oppositely to control system-imposed variations of A.

The means referred to in the preceding sentence can be provided by causing the optimizing action to proceed in steps, according to fixed sequence. Refer now to FIG. 4, which is a schematic illustration of a maximized heat exchange computer arranged to handle variable total flow rates. In FIG. 4, elements the same as those previously described are denoted by the same reference numerals.

In FIG. 4, the flow recording controller 9 has an electrically-adjustable set point S.P., which is adapted to be changed by a fixed amount in response to a pulse supplied to this set point control from a unit pulse transmitter 73. The direction of change of this set point depends upon the relative sense of the pulse supplied from transmitter 73.

The flow B is regulated by a ow recording controller 74 having a mechanically-adjustable set point S.P. The ow transmitter 12 feeds its signal into controller 74. The flow B to heat exchanger 2 passes through a flow control valve 75. Controller 74 controls or operates valve 75 (this control being represented by a dotted-line connection) to maintain flow B at the rate determined by the adjustment of the set point of controller 74. How this set point is automatically adjusted will be detailed hereinafter.

Just as in FIG. 1, the output 8 of the circuit 7 represents ilow A, while the output 14 of the circuit 13 represents dow B. These two iiows A and B are supplied to an add circuit 76, wherein the measurements are added to provide an output 77 of A+B. This output signal (A +B) at 77 is fed by way of the movable arm of a switch 78 (when this switch arm is on its left-hand contact, as illustrated in FIG. 4) to a storage unit 79, which stores its value. Storage unit 79 may be similar to storage unit 61 in FIG. 3. The signal stored in unit 79 is fed to a subtract circuit 80.

A sequencer S1 is coupled to switch 78, to a servo drive circuit 82, and to a maximized heat exchange computer 83, as indicated by the dotted-line connections 84, 8S, and 86, respectively.

The heat exchange computer 83 would be arranged internally as shown in FIG. 1 (and would be supplied with temperature and ow measurements, as in this latter ligure), except that the computer output wo'uld not be to the reversing motor drive 46 of FIG. 1, but would be instead to the unit pulse transmitter 73, as shown in FIG. 4. The unit pulse transmitter 73 can supply pulses to the set point control of controller 9 by way of a connection 87.

After the total flow A+B has been measured and stored in storage unit 79, sequencer 81 sends out impulses which (by way of connection S4) operate switch 78 to disconnect the A+B signal from unit 79, and which (by way of connection 36) activate the computer S3.

The computer 83, when activated, operates as previously described (in connection with FIG. l) to develop an output 45 proportional to dQ/dA, and this output is fed to unit pulse transmitter 73. It dQ/dA is not zero, pulse transmitter 73 produces a pulse of a particular sense which depends upon the calculated sign (positive or negative) of dQ/dA, as calculated by computed 83. The unit pulse transmitter 73 transmits this produced pulse to the set-point control of controller 9 in stream A.

When computer 83 is activated, the unit pulse transmitter 73 changes the set point of ow controller 9 by a fixed amount in the appropriate direction, according to the calculated sign of iQ/dA. This change of the set point is effected by means of the pulse transmitted from transmitter 73 to controller 9, by way of connection 87. Of course, this change of the set point of controller 9 results in a new value for ilow A.

After the pulse is transmitted to controller 9, sequencer 81 disconnects (deactivates or deenergizes) computer 83, and operaes switch 78 to its right-hand contact, thereby to switch the (new) A+B signal to subtract circuit 80. Also, by way of connection S5, sequencer 81 at this time turns on the servo drive 82. The mechanical output of servo drive S2 is connected to the set-point control of the tlow controller 74 in stream B, as indicated by the dottedline connection 88.

At this juncture, storage unit 79 contains the old value of A+B; this signal is fed continuously to subtract circuit 80. The subtract circuit Si) now subtracts from this the new value of A+B (which is fed to this circuit when switch 78 is on its right-hand Contact). The difference (output S9 of circuit 89), which is the change in flow A, is fed to the input of servo drive unit 82. The input signal to servo drive 82 causes this servo ldrive to mechanically adjust the set point of the ow B controller 74 so as to change llow B and bring this diierence (output 89 of circuit Stl) to zero. When this latter diierence is zero (or after a set time), sequencer 81 turns otf the servo drive 32 and operates switch 78 back to its left-hand contact, thereby to switch the A+B signal back to storage unit 79, and start the cycle again. Y

Summarizing, the FIG. 4 arrangement will provide an optimum (maximum heat transferred) ow division even when the total ow varies, by means of the following operating steps: 1) measuring and storing the initial (or original) value of total flow A+B, (2) calculating dQ/dA, (3) setting flow A a unit amount toward zero dQ/dA, (4) measuring the new total flow A+B, (5) comparing is new ow with the old or original, and (6) adjusting flow B to make the new ow A+B equal the old flow A+B. Then, the cycle is repeated, starting with step (l) above.

Although there has previously been described a heat exchange system wherein the temperature of the main stream is being raised, it will be understood that the same control system, With certain obvious modifications of the mathematics, will also maximize the heat transfer (to minimize the outlet temperature) in an arrangement wherein a stream is being cooled with parallel-connected exchangers.

The description up to this point has dealt with only a single pair of parallel-connected heat exchangers. It will now be explained how a control system or control scheme which optimizes the heat exchange of a pair of parallelconnected heat exchangers can be extended and cornbined to yield a system which can optimize the heat ex'- change of any number of parallel-connected heat exchangers.

Consider Ia system of three parallel-connected heat exchanges X, Y, and Z which are piped together as shown in FIG. 5, 'with exchangers X and Y being paired so that the total stream at 9@ is tirst split at 91 between exchangers X and Y combined and Z separate, and the output streams from exchangers X and Y are joined together at 92 before being joined 'at 93 to the output of exchanger Z. In this case, it is clear that any of the control schemes previously disclosed (in FIGS. l, 2, or 4) can -be applied to the control of the exchanger pair X and Y, and such scheme will divid the ow between them to optimize the heat exchanger of this pair aone, for the particular total flow they are handling. Now, an additional control scheme (any of those disclosed in FIGS. l, 2, or 4 above) can be applied to the pair .made up of Z and X plus Y, where the combination of X plus Y is treated as a single exchanger.

The foregoing is illustrated in FIG. 5, wherein in ternal Control Scheme I (indicated by 'a dotted-line enclosure) deals with the exchanger pair X and Y, and external Control Scheme II (also indicated by a dottedline enclosure) deals with the exchanger pair Z and X plus Y treated as a single exchanger.

In the manner just described, by adding an external control scheme for each added heat exchanger, the control schemes described hereinabove (in connection with FIGS. 1, 2, and 4) as applying to a pair of exchangers can be extended to control any number of exchangers in parallel.

In practice, the time constants of the several control loops and the associated exchangers must be selected to have appropriate relationships, to avoid instabilities in operation.

FIG. 5 illustrates the three exchangers as piped together in a somewhat unusual way, this having been done mainly to illustrate the idea of the grouping of X with Y and then this pair with Z. Ordinarily, a control scheme must conform to a piping system as it exists, and it is possible that exchangers will be so piped together that there is no natural grouping of exchangers into pairs with clearly dened points of measurement of the combined streams. However, most common piping systems will exhibit pairing arrangements in which the necessary measuring points are accessible. Examples of some common piping systems are shown in FIGS. 6, 7, and 9.

In FIG. 6, exchangers X and Y would be grouped together as a pair and a first control scheme applied to this pair; then a second control scheme would deal with the exchanger pair Z and X plus Y treated as a single exchanger.

In FIG. 7, exchangers Y and Z would be grouped together as a pair and a irst control scheme applied to h is pair; then a second control scheme would deal with he exchanger pair X and Y plus Z treated as a single :xchangerl In FIG. 9, exchangers X and Y would be grouped ogether as a pair and a first control scheme applied to his pair; then a second control scheme would deal with he exchanger pair" Z and X plus Y treated as a single axchanger.

However, -it is possible that a set of parallel-connected leat exchangers may be so piped together that there is 1o apparent grouping into a first pair followed by suc- :essive additions of single exchangers. This apparent grouping is based on the ability to measure the neces- ;ary flows and temperatures. While the control schemes )f FIGS. l, 2, and 4 require only the measurement of the ieparate flow through each of the members of a pair of Jarallel-connected exchangers (never the total ow :hrough both members), and only the measurement of the empera-tures of the separate output streams from the two :xchangers of the pair (never the temperature of the outiut stream after blending), these values of total ow and Jlended temperature are needed when a pair of exchangzrs is to be treated as a single exchanger, Since the streams o and from each exchanger must be separated at least it the point of entry to and exit from each exchanger, it vill always be possible to measure the entrance and exit .emperatures, and the rate of ow of each separate stream, :'or each separate exchanger. The difficulty will arise in :ases where the joined piping runs preceding or followng an exchanger pair are both too short to permit a good measurement of the total iiow rate for the pair, or where he joined piping run following an exchanger pair is too .hort to provide a good blending of the two exchanger utputs, so that a blended temperature cannot be measired before the stream from -the third exchanger is mixed n. FIG. 8 is one symbolic diagram of such an assembly where the connections to and from exchangers X, Y, Z are iubstantially at single points so that no pair measurenents of ow yand temperature can be made. Note that the nput temperature for a battery of parallel-connected ex- :hangers is the same for all exchangers, and is generally iccessible for measurement.

In cases of the type referred to in the preceding paragraph, recourse may be had to Lautomatic calculation, o obtain the unmeasurable total flows or blended temperttures from the individual ows and temperatures. This s illustrated in FIG. 10. In FIG. 10, the piping is such :see the large-diameter input manifold pipe 94 and the arge-diameter output manifold pipe 95) that it is imiossible to obtain good direct measurements of the total low rate f(X+Y) for the pair of yheat exchangers X and Y, )r of the blended temperature T(X+Y) of this same pair )f exchangers. In FIG. l0, T1 represents the temperature )f the total input stream, fx, fy, and fz represent the ne-asured ow rates through exchangers X, Y, and Z, and FX, Ty, and TZ represent the measured temperatures of he output streams from exchangers X, Y, and Z. The low transmitter 6, coupled to flowmeter 5, transmits the neasured ow rate fx to a simple computer 96 (e.g., an idder). Similarly, the flow transmitter 12, coupled to lowmeter 11, transmits the measured flow rate Y to com- )uter 96. The computer 96 adds the measurements fx and :Y to give the total flow rate f X+Y through exchangers l and Y combined.

The flow transmitters 6 and 12 also transm-it their re- :pective flow rate measurements to a somewhat more :omplex blend computer 97. The temperature-sensing elenent 1S supplies its temperature measurement TX to comiuter 97. Similarly, the temperature-sensing element 19 upplies its temperature measurement TY to computer 97. ['he computer 97 combines the flow rate and temperature neasurements supplied to it (with stored information :oncerning the properties of the flowing material) into a calculated value of the temperature T(X+Y) `of the blended output streams from exchangers X and Y.

The devices 96 and 97 thus will provide the flow and temperature information required to treat the pair of exchangers X and Y as a single exchanger, for the purpose of determining the optimum (for maximum transfer of heat) ow division between these two and exchanger Z.

The arrangements described previously (in connection with FIGS. 5-l0), where two exchangers are paired and then each additional exchanger is added as a new member of a pair, will work for any number of exchangers, and will require (n-l) control schemes, where n is the number of parallel-connected exchangers. Other arrangements are possible, however. One such is illustrated in FIG. ll, wherein eight parallel-connected exchangers are controlled first by pairing the mall (Control Schemes I, II, III, and IV), then by pairing the pairs (Control Schemes V and VI), and then by pairing the pairs of pairs (Control Scheme VII). This requires the same number of control schemes as would be required by the addone-at-a-time plan, but offers some advantage in the depth of nesting of control schemes. That is to say, in FIG. ll there are only three levels of control schemes (inner Schemes I, II, III, and IV; middle Schemes V and VI; outer Scheme VII), whereas had the add-one-at-a-time plan been utilized, there would have been seven such levels. Since the problem of stability of nested control schemes is related to the depth of nesting, the plan of FIG. ll may be preferable when more than three parallelconnected exchangers are involved.

In considering the number of control schemes or control systems required for a set of parallel-connected exchangers, the possibility of timesharing all or part of the computational facilities should not be overlooked. A switching scheme could `be employed to successively switch lparts of the computing equipment (e.g., the maximized heat exchanger computers of FIGS. l or 2) from one control scheme to another, so that a single computer could service several control schemes.

The invention claimed is:

1. A control system for maximizing the total heat transferred to a fluid flowing through two parallel-connected heat exchanger assemblies one of which may comprise a plurality of exchangers connected in parallel, said system comprising separate means for measuring the individual rate of ow through each exchanger assembly, means for measuring the huid outlet temperature of each exchanger assembly, means combining, in accordance with a predetermined mathematical formula, the aforesaid measurements with the predetermined iiuid outlet temperature vs. fluid i'iow characteristics of the two exchanger assemblies to develop a control signal pro-portional to the rate of change of the total heat transferred with a change in the uid ow throughthe first exchanger assembly, and means acting in response to said control signal for controlling the fluid flow through one of said exchanger assemblies.

2. System as set forth in claim 1, wherein the fluid iiow through said rst exchanger assembly is controlled in response ot said control signal.

3. System as set forth in claim 1, wherein the direction of the control of the :fluid ow through said one exchanger assembly is such as to cause the value of said control signal to approach zero.

4. System as set forth in claim 2, wherein the direction of the control of the liuid ow through said first exchanger assembly is such as to cause the value of said control signal to approach zero.

5. A control system for maximizing the total heat transferred to a fluid flowing through two parallel-connected heat exchanger assemblies one of which may comprise a plurality of heat exchangers connected in parallel, said system comprising means for measuring the rate of iiow A through the first exchanger assembly, means for measuring the rate of flow B through the second exchanger assembly, means for measuring the fluid outlet temperature TA of the rst exchanger assembly, means for measuring the fluid outlet temperature TB of the second exchanger assembly, means combining the aforesaid measurements with the Ipredetermined fluid outlet temperature vs. uid flow characteristics of the two exchanger assen1- blies in accordance with the following formula thereby to develop a resultant signal for control purposes:

where K2 is a constant appropriate to the fluid, and means controlling the fluid ow through one of said exchanger assemblies in response to said control signal.

`6. A control system for maximizing the total heat transferred to a fluid flowing through two parallel-connected heat exchanger assemblies one of which may comprise a plurality of heat exchangers connected in parallel, said system comprising means for measuring the rate of ow A through the first exchanger assembly, means for measuring the rate of flow B through the second exchanger assembly, means for measuring the uid outlet temperature TA f the irst exchanger assembly, means for measuring the fluid outlet temperature TB of the second exchanger assembly, means combining the aforesaid measurements with the predetermined uid outlet temperature vs. fluid flow characteristics of the two exchanger assemblies in accordance with the following formula, thereby to develop a resultant signal for control purposes: TA(K2+TAl-TB) -TBUz-i-TA-l- TB) -l- AdTA dTB Where K2 is a constant appropriate to the fluid, and

means controlling the fluid ow A through said first exchanger assembly in response to said control signal.

7. A control system for maximizing the total heat transferred to a uid owing through two parallel-connected heat exchanger assemblies one of which may com prise a plurality of heat exchangers connected in parallel, said system comprising means for measuring the rate of flow A through the iirst exchanger assembly, means for measuring the rate of flow B through the second exchanger assembly, means for measuring the fluid outlet temperature TA of the rst exchanger assembly, means for measuring the uid outlet temperature TB of the second exchanger assembly, means combining the aforesaid measurements with the predetermined uid outlet temprature vs. fluid ow characteristics of the two exchanger assemblies in accordance with the following formula, thereby to develop a resultant signal for control purposes:

where K2 is a constant appropriate to the fluid, and means controlling the uid ow through one of said exchanger assemblies, in response to said control signal, in such a direction as to cause the value of said control signal to approach zero.

References Cited UNITED STATES PATENTS 2,761,284 9/1956 Malick 235-150.1 X 2,976,234 3/1961 Webber 202-160 X 3,079,079 2/ 1963 Phister et al. 23S-150.1 3,150,064 9/1964 Dobson 202-160 X 3,167,113 l/1965 Kleiss 23S-150.1 X 3,174,298 3/1965 Kleiss 137-98 X MALCOLM A. MORRISON, Primary Examiner.

I. KESCHNER, Assistant Examiner. 

1. A CONTROL SYSTEM FOR MAXIMIZING THE TOTAL HEAT TRANSFERRED TO A FLUID FLOWING THROUGH TWO PARALLEL-CONNECTED HEAT EXCHANGER ASSEMBLIES ONE OF WHICH MAY COMPRISE A PLURALITY OF EXCHANGERS CONNECTED IN PARALLEL, SAID SYSTEM COMPRISING SEPARATE MEANS FOR MEASURING THE INDIVIDUAL RATE TO FLOW THROUGH EACH EXCHANGER ASSEMBLY, MEANS FOR MEASURING THE FLUID OUTLET TEMPERATURE OF EACH EXCHANGER ASSEMBLY, MEANS COMBINING, IN ACCORDANCE WITH A PREDETERMINED MATHEMATICAL FORMULA, THE AFORESAID MEASUREMENTS WITH THE PREDETERMINED FLUID OUTLET TEMPERTURE VS. FLUID FLOW CHARACTERISTICS OF THE TWO EXCHANGER ASSEMBLIES TO DEVELOP A CONTROL SIGNAL PROPORTIONAL TO THE RATE OF CHANGE OF THE TOTAL HEAT TRANSFERRED WITH A CHANGE IN THE FLUID FLOW THROUGH THE FIRST EXCHANGER ASSEMBLY, AND MEANS ACTING IN RESPONSE TO SAID CONTROL SIGNAL FOR CONTROLLING THE FLUID FLOW THROUGH ONE OF SAID EXCHANGER ASSEMBLIES. 